login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235391 Expansion of 2 / (2 - x / sqrt(1 - 4*x)). 1
1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895, 322037615290, 1305256267511, 5293166568270, 21475362822956, 87166344495561, 353933533606927 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1 / (1 - x / (1 - x / (1 - 2*x / (1 - x / (2 - 3*x / (1 - 2*x / (3 - 4*x / ... ))))))).

D-finite with recurrence: 0 = (4*n + 6) * a(n) - (17*n + 27) * a(n+1) + (24*n + 42) * a(n+2) - (9*n + 21) * a(n+3) + (n + 3) * a(n+4). - Sign flipped by R. J. Mathar, Feb 16 2020

0 = a(n) * (16*a(n+1) - 74*a(n+2) + 120*a(n+3) - 66*a(n+4) + 10*a(n+5))+ a(n+1) * (-62*a(n+1) + 361*a(n+2) - 480*a(n+3) + 265*a(n+4) - 41*a(n+5)) + a(n+2) * (-342*a(n+2) + 615*a(n+3) - 335*a(n+4) + 54*a(n+5)) + a(n+3) * (-90*a(n+3) + 75*a(n+4) - 15*a(n+5)) + a(n+4) * (-3*a(n+4) + a(n+5)).

a(n) = A129775(n) if n>0.

HANKEL transform is A000012.

INVERT transform is A073525.

EXAMPLE

G.f. = 1 + x + 2*x^2 + 6*x^3 + 21*x^4 + 78*x^5 + 298*x^6 + 1157*x^7 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ 2 / (2 - x - x / Sqrt[1 - 4 x]), {x, 0, n}]

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( 2 / (2 - x - x / sqrt(1 - 4*x + x * O(x^n))), n))}

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!(2/( 2-x - x/Sqrt(1-4*x)))); // G. C. Greubel, Aug 07 2018

CROSSREFS

Cf. A000012, A073525, A129775.

Sequence in context: A277221 A129776 A129775 * A254316 A279562 A054515

Adjacent sequences:  A235388 A235389 A235390 * A235392 A235393 A235394

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 09 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 16:17 EST 2021. Contains 349445 sequences. (Running on oeis4.)